/*
* jidctint.c
*
* Copyright (C) 1991-1998, Thomas G. Lane.
* This file is part of the Independent JPEG Group's software.
* For conditions of distribution and use, see the accompanying README file.
*
* This file contains a slow-but-accurate integer implementation of the
* inverse DCT (Discrete Cosine Transform).  In the IJG code, this routine
* must also perform dequantization of the input coefficients.
*
* A 2-D IDCT can be done by 1-D IDCT on each column followed by 1-D IDCT
* on each row (or vice versa, but it's more convenient to emit a row at
* a time).  Direct algorithms are also available, but they are much more
* complex and seem not to be any faster when reduced to code.
*
* This implementation is based on an algorithm described in
*   C. Loeffler, A. Ligtenberg and G. Moschytz, "Practical Fast 1-D DCT
*   Algorithms with 11 Multiplications", Proc. Int'l. Conf. on Acoustics,
*   Speech, and Signal Processing 1989 (ICASSP '89), pp. 988-991.
* The primary algorithm described there uses 11 multiplies and 29 adds.
* We use their alternate method with 12 multiplies and 32 adds.
* The advantage of this method is that no data path contains more than one
* multiplication; this allows a very simple and accurate implementation in
* scaled fixed-point arithmetic, with a minimal number of shifts.
*/

#define JPEG_INTERNALS
#include "jinclude.h"
#include "jpeglib.h"
#include "jdct.h"		/* Private declarations for DCT subsystem */

#ifdef DCT_ISLOW_SUPPORTED


/*
* This module is specialized to the case DCTSIZE = 8.
*/

#if DCTSIZE != 8
Sorry, this code only copes with 8x8 DCTs. /* deliberate syntax err */
#endif


/*
* The poop on this scaling stuff is as follows:
*
* Each 1-D IDCT step produces outputs which are a factor of sqrt(N)
* larger than the true IDCT outputs.  The final outputs are therefore
* a factor of N larger than desired; since N=8 this can be cured by
* a simple right shift at the end of the algorithm.  The advantage of
* this arrangement is that we save two multiplications per 1-D IDCT,
* because the y0 and y4 inputs need not be divided by sqrt(N).
*
* We have to do addition and subtraction of the integer inputs, which
* is no problem, and multiplication by fractional constants, which is
* a problem to do in integer arithmetic.  We multiply all the constants
* by CONST_SCALE and convert them to integer constants (thus retaining
* CONST_BITS bits of precision in the constants).  After doing a
* multiplication we have to divide the product by CONST_SCALE, with proper
* rounding, to produce the correct output.  This division can be done
* cheaply as a right shift of CONST_BITS bits.  We postpone shifting
* as long as possible so that partial sums can be added together with
* full fractional precision.
*
* The outputs of the first pass are scaled up by PASS1_BITS bits so that
* they are represented to better-than-integral precision.  These outputs
* require BITS_IN_JSAMPLE + PASS1_BITS + 3 bits; this fits in a 16-bit word
* with the recommended scaling.  (To scale up 12-bit sample data further, an
* intermediate INT32 array would be needed.)
*
* To avoid overflow of the 32-bit intermediate results in pass 2, we must
* have BITS_IN_JSAMPLE + CONST_BITS + PASS1_BITS <= 26.  Error analysis
* shows that the values given below are the most effective.
*/

#if BITS_IN_JSAMPLE == 8
#define CONST_BITS  13
#define PASS1_BITS  2
#else
#define CONST_BITS  13
#define PASS1_BITS  1		/* lose a little precision to avoid overflow */
#endif

/* Some C compilers fail to reduce "FIX(constant)" at compile time, thus
* causing a lot of useless floating-point operations at run time.
* To get around this we use the following pre-calculated constants.
* If you change CONST_BITS you may want to add appropriate values.
* (With a reasonable C compiler, you can just rely on the FIX() macro...)
*/

#if CONST_BITS == 13
#define FIX_0_298631336  ((INT32)  2446)	/* FIX(0.298631336) */
#define FIX_0_390180644  ((INT32)  3196)	/* FIX(0.390180644) */
#define FIX_0_541196100  ((INT32)  4433)	/* FIX(0.541196100) */
#define FIX_0_765366865  ((INT32)  6270)	/* FIX(0.765366865) */
#define FIX_0_899976223  ((INT32)  7373)	/* FIX(0.899976223) */
#define FIX_1_175875602  ((INT32)  9633)	/* FIX(1.175875602) */
#define FIX_1_501321110  ((INT32)  12299)	/* FIX(1.501321110) */
#define FIX_1_847759065  ((INT32)  15137)	/* FIX(1.847759065) */
#define FIX_1_961570560  ((INT32)  16069)	/* FIX(1.961570560) */
#define FIX_2_053119869  ((INT32)  16819)	/* FIX(2.053119869) */
#define FIX_2_562915447  ((INT32)  20995)	/* FIX(2.562915447) */
#define FIX_3_072711026  ((INT32)  25172)	/* FIX(3.072711026) */
#else
#define FIX_0_298631336  FIX(0.298631336)
#define FIX_0_390180644  FIX(0.390180644)
#define FIX_0_541196100  FIX(0.541196100)
#define FIX_0_765366865  FIX(0.765366865)
#define FIX_0_899976223  FIX(0.899976223)
#define FIX_1_175875602  FIX(1.175875602)
#define FIX_1_501321110  FIX(1.501321110)
#define FIX_1_847759065  FIX(1.847759065)
#define FIX_1_961570560  FIX(1.961570560)
#define FIX_2_053119869  FIX(2.053119869)
#define FIX_2_562915447  FIX(2.562915447)
#define FIX_3_072711026  FIX(3.072711026)
#endif


/* Multiply an INT32 variable by an INT32 constant to yield an INT32 result.
* For 8-bit samples with the recommended scaling, all the variable
* and constant values involved are no more than 16 bits wide, so a
* 16x16->32 bit multiply can be used instead of a full 32x32 multiply.
* For 12-bit samples, a full 32-bit multiplication will be needed.
*/

#if BITS_IN_JSAMPLE == 8
#define MULTIPLY(var,const)  MULTIPLY16C16(var,const)
#else
#define MULTIPLY(var,const)  ((var) * (const))
#endif


/* Dequantize a coefficient by multiplying it by the multiplier-table
* entry; produce an int result.  In this module, both inputs and result
* are 16 bits or less, so either int or short multiply will work.
*/

#define DEQUANTIZE(coef,quantval)  (((ISLOW_MULT_TYPE) (coef)) * (quantval))


/*
* Perform dequantization and inverse DCT on one block of coefficients.
*/

GLOBAL(void)
jpeg_idct_islow (j_decompress_ptr cinfo, jpeg_component_info * compptr,
				 JCOEFPTR coef_block,
				 JSAMPARRAY output_buf, JDIMENSION output_col)
{
	INT32 tmp0, tmp1, tmp2, tmp3;
	INT32 tmp10, tmp11, tmp12, tmp13;
	INT32 z1, z2, z3, z4, z5;
	JCOEFPTR inptr;
	ISLOW_MULT_TYPE * quantptr;
	int * wsptr;
	JSAMPROW outptr;
	JSAMPLE *range_limit = IDCT_range_limit(cinfo);
	int ctr;
	int workspace[DCTSIZE2];	/* buffers data between passes */
	SHIFT_TEMPS

		/* Pass 1: process columns from input, store into work array. */
		/* Note results are scaled up by sqrt(8) compared to a true IDCT; */
		/* furthermore, we scale the results by 2**PASS1_BITS. */

		inptr = coef_block;
	quantptr = (ISLOW_MULT_TYPE *) compptr->dct_table;
	wsptr = workspace;
	for (ctr = DCTSIZE; ctr > 0; ctr--) {
		/* Due to quantization, we will usually find that many of the input
		* coefficients are zero, especially the AC terms.  We can exploit this
		* by short-circuiting the IDCT calculation for any column in which all
		* the AC terms are zero.  In that case each output is equal to the
		* DC coefficient (with scale factor as needed).
		* With typical images and quantization tables, half or more of the
		* column DCT calculations can be simplified this way.
		*/

		if (inptr[DCTSIZE*1] == 0 && inptr[DCTSIZE*2] == 0 &&
			inptr[DCTSIZE*3] == 0 && inptr[DCTSIZE*4] == 0 &&
			inptr[DCTSIZE*5] == 0 && inptr[DCTSIZE*6] == 0 &&
			inptr[DCTSIZE*7] == 0) {
				/* AC terms all zero */
				int dcval = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]) << PASS1_BITS;

				wsptr[DCTSIZE*0] = dcval;
				wsptr[DCTSIZE*1] = dcval;
				wsptr[DCTSIZE*2] = dcval;
				wsptr[DCTSIZE*3] = dcval;
				wsptr[DCTSIZE*4] = dcval;
				wsptr[DCTSIZE*5] = dcval;
				wsptr[DCTSIZE*6] = dcval;
				wsptr[DCTSIZE*7] = dcval;

				inptr++;			/* advance pointers to next column */
				quantptr++;
				wsptr++;
				continue;
		}

		/* Even part: reverse the even part of the forward DCT. */
		/* The rotator is sqrt(2)*c(-6). */

		z2 = DEQUANTIZE(inptr[DCTSIZE*2], quantptr[DCTSIZE*2]);
		z3 = DEQUANTIZE(inptr[DCTSIZE*6], quantptr[DCTSIZE*6]);

		z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
		tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
		tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);

		z2 = DEQUANTIZE(inptr[DCTSIZE*0], quantptr[DCTSIZE*0]);
		z3 = DEQUANTIZE(inptr[DCTSIZE*4], quantptr[DCTSIZE*4]);

		tmp0 = (z2 + z3) << CONST_BITS;
		tmp1 = (z2 - z3) << CONST_BITS;

		tmp10 = tmp0 + tmp3;
		tmp13 = tmp0 - tmp3;
		tmp11 = tmp1 + tmp2;
		tmp12 = tmp1 - tmp2;

		/* Odd part per figure 8; the matrix is unitary and hence its
		* transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
		*/

		tmp0 = DEQUANTIZE(inptr[DCTSIZE*7], quantptr[DCTSIZE*7]);
		tmp1 = DEQUANTIZE(inptr[DCTSIZE*5], quantptr[DCTSIZE*5]);
		tmp2 = DEQUANTIZE(inptr[DCTSIZE*3], quantptr[DCTSIZE*3]);
		tmp3 = DEQUANTIZE(inptr[DCTSIZE*1], quantptr[DCTSIZE*1]);

		z1 = tmp0 + tmp3;
		z2 = tmp1 + tmp2;
		z3 = tmp0 + tmp2;
		z4 = tmp1 + tmp3;
		z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

		tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
		tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
		tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
		tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
		z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
		z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
		z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
		z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */

		z3 += z5;
		z4 += z5;

		tmp0 += z1 + z3;
		tmp1 += z2 + z4;
		tmp2 += z2 + z3;
		tmp3 += z1 + z4;

		/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

		wsptr[DCTSIZE*0] = (int) DESCALE(tmp10 + tmp3, CONST_BITS-PASS1_BITS);
		wsptr[DCTSIZE*7] = (int) DESCALE(tmp10 - tmp3, CONST_BITS-PASS1_BITS);
		wsptr[DCTSIZE*1] = (int) DESCALE(tmp11 + tmp2, CONST_BITS-PASS1_BITS);
		wsptr[DCTSIZE*6] = (int) DESCALE(tmp11 - tmp2, CONST_BITS-PASS1_BITS);
		wsptr[DCTSIZE*2] = (int) DESCALE(tmp12 + tmp1, CONST_BITS-PASS1_BITS);
		wsptr[DCTSIZE*5] = (int) DESCALE(tmp12 - tmp1, CONST_BITS-PASS1_BITS);
		wsptr[DCTSIZE*3] = (int) DESCALE(tmp13 + tmp0, CONST_BITS-PASS1_BITS);
		wsptr[DCTSIZE*4] = (int) DESCALE(tmp13 - tmp0, CONST_BITS-PASS1_BITS);

		inptr++;			/* advance pointers to next column */
		quantptr++;
		wsptr++;
	}

	/* Pass 2: process rows from work array, store into output array. */
	/* Note that we must descale the results by a factor of 8 == 2**3, */
	/* and also undo the PASS1_BITS scaling. */

	wsptr = workspace;
	for (ctr = 0; ctr < DCTSIZE; ctr++) {
		outptr = output_buf[ctr] + output_col;
		/* Rows of zeroes can be exploited in the same way as we did with columns.
		* However, the column calculation has created many nonzero AC terms, so
		* the simplification applies less often (typically 5% to 10% of the time).
		* On machines with very fast multiplication, it's possible that the
		* test takes more time than it's worth.  In that case this section
		* may be commented out.
		*/

#ifndef NO_ZERO_ROW_TEST
		if (wsptr[1] == 0 && wsptr[2] == 0 && wsptr[3] == 0 && wsptr[4] == 0 &&
			wsptr[5] == 0 && wsptr[6] == 0 && wsptr[7] == 0) {
				/* AC terms all zero */
				JSAMPLE dcval = range_limit[(int) DESCALE((INT32) wsptr[0], PASS1_BITS+3)
					& RANGE_MASK];

				outptr[0] = dcval;
				outptr[1] = dcval;
				outptr[2] = dcval;
				outptr[3] = dcval;
				outptr[4] = dcval;
				outptr[5] = dcval;
				outptr[6] = dcval;
				outptr[7] = dcval;

				wsptr += DCTSIZE;		/* advance pointer to next row */
				continue;
		}
#endif

		/* Even part: reverse the even part of the forward DCT. */
		/* The rotator is sqrt(2)*c(-6). */

		z2 = (INT32) wsptr[2];
		z3 = (INT32) wsptr[6];

		z1 = MULTIPLY(z2 + z3, FIX_0_541196100);
		tmp2 = z1 + MULTIPLY(z3, - FIX_1_847759065);
		tmp3 = z1 + MULTIPLY(z2, FIX_0_765366865);

		tmp0 = ((INT32) wsptr[0] + (INT32) wsptr[4]) << CONST_BITS;
		tmp1 = ((INT32) wsptr[0] - (INT32) wsptr[4]) << CONST_BITS;

		tmp10 = tmp0 + tmp3;
		tmp13 = tmp0 - tmp3;
		tmp11 = tmp1 + tmp2;
		tmp12 = tmp1 - tmp2;

		/* Odd part per figure 8; the matrix is unitary and hence its
		* transpose is its inverse.  i0..i3 are y7,y5,y3,y1 respectively.
		*/

		tmp0 = (INT32) wsptr[7];
		tmp1 = (INT32) wsptr[5];
		tmp2 = (INT32) wsptr[3];
		tmp3 = (INT32) wsptr[1];

		z1 = tmp0 + tmp3;
		z2 = tmp1 + tmp2;
		z3 = tmp0 + tmp2;
		z4 = tmp1 + tmp3;
		z5 = MULTIPLY(z3 + z4, FIX_1_175875602); /* sqrt(2) * c3 */

		tmp0 = MULTIPLY(tmp0, FIX_0_298631336); /* sqrt(2) * (-c1+c3+c5-c7) */
		tmp1 = MULTIPLY(tmp1, FIX_2_053119869); /* sqrt(2) * ( c1+c3-c5+c7) */
		tmp2 = MULTIPLY(tmp2, FIX_3_072711026); /* sqrt(2) * ( c1+c3+c5-c7) */
		tmp3 = MULTIPLY(tmp3, FIX_1_501321110); /* sqrt(2) * ( c1+c3-c5-c7) */
		z1 = MULTIPLY(z1, - FIX_0_899976223); /* sqrt(2) * (c7-c3) */
		z2 = MULTIPLY(z2, - FIX_2_562915447); /* sqrt(2) * (-c1-c3) */
		z3 = MULTIPLY(z3, - FIX_1_961570560); /* sqrt(2) * (-c3-c5) */
		z4 = MULTIPLY(z4, - FIX_0_390180644); /* sqrt(2) * (c5-c3) */

		z3 += z5;
		z4 += z5;

		tmp0 += z1 + z3;
		tmp1 += z2 + z4;
		tmp2 += z2 + z3;
		tmp3 += z1 + z4;

		/* Final output stage: inputs are tmp10..tmp13, tmp0..tmp3 */

		outptr[0] = range_limit[(int) DESCALE(tmp10 + tmp3,
			CONST_BITS+PASS1_BITS+3)
			& RANGE_MASK];
		outptr[7] = range_limit[(int) DESCALE(tmp10 - tmp3,
			CONST_BITS+PASS1_BITS+3)
			& RANGE_MASK];
		outptr[1] = range_limit[(int) DESCALE(tmp11 + tmp2,
			CONST_BITS+PASS1_BITS+3)
			& RANGE_MASK];
		outptr[6] = range_limit[(int) DESCALE(tmp11 - tmp2,
			CONST_BITS+PASS1_BITS+3)
			& RANGE_MASK];
		outptr[2] = range_limit[(int) DESCALE(tmp12 + tmp1,
			CONST_BITS+PASS1_BITS+3)
			& RANGE_MASK];
		outptr[5] = range_limit[(int) DESCALE(tmp12 - tmp1,
			CONST_BITS+PASS1_BITS+3)
			& RANGE_MASK];
		outptr[3] = range_limit[(int) DESCALE(tmp13 + tmp0,
			CONST_BITS+PASS1_BITS+3)
			& RANGE_MASK];
		outptr[4] = range_limit[(int) DESCALE(tmp13 - tmp0,
			CONST_BITS+PASS1_BITS+3)
			& RANGE_MASK];

		wsptr += DCTSIZE;		/* advance pointer to next row */
	}
}

#endif /* DCT_ISLOW_SUPPORTED */
